Essays on the Hicks-Sraffa Supermultiplier Considering Autonomous Export and the Labor Market
Pós-Keynesiano; Estabilidade; Bifurcação de Hopf; Supermultiplicador Sraffiano
The present Thesis is divided into four chapters, each of which are independent, but have common objectives; they are: to analyze how the Sraffian Supermultiplier (SSM) was formed and how it behaves considering exports as an alternative proposal to autonomous consumption and including the labor market. The first chapter seeks to present the historical context of the formation of the SSM and how the national and international debate on the subject has been treated. For this, it was exposed that the original theory was based on the work of Sraffa and Garegnani; however, it was only formalized in the mid-1990s. The model published at the time proposes that economic growth must necessarily consider that the autonomous consumption of capitalists is responsible for determining the progress of economies. However, this proposal did not satisfy all critical thinkers of post-Keynesianism who, from Lavoie's work in 2015, have generated an extensive debate. The arguments and replies aim to verify if, in fact, the theory is efficient in considering this autonomous component as a guarantor of sustainable growth and the convergence of the utilization capacity to its normal level. The second chapter proposes a new approach considering two different autonomous components, exports and consumption, generating three different cases: (I) when the growth of exports (𝑔𝑋) is equal to the growth of autonomous consumption (𝑔𝑋); (II) 𝑔𝑋 > 𝑔𝑍; and (III) 𝑔𝑋 < 𝑔𝑍. Through this new model, the stability conditions and the existence of a Hopf bifurcation were analyzed for the three cases; however, only in the last two is it possible to guarantee stability and bifurcation. Furthermore, the robustness of the model proposed in this chapter is proved through numerical simulations and, with the use of the computational approach, the results of the endogenous cycle can be guaranteed. The third chapter seeks to contribute to the literature by proposing that labor supply, in the long-run, is not necessarily perfectly elastic, so that, in a special case, it may be perfectly inelastic. This hypothesis generates a significant difference with the traditional postKeynesian approach that, primarily, does not consider that the labor supply can be limited to values lower than the full capacity of using the factors in the long term. With this, it is possible to verify how the behavior occurs on both sides, productivity and demand, under the hypothesis of restricted work. As a result, this modification showed that, in its original form, SSM cannot sustain growth without generating excess demand and increasing labor shortages. The fourth chapter makes the labor market hypothesis in the original version of the model more flexible, showing how the elasticity of labor supply (and thus, not considering any of the extreme cases above), affects productivity and aggregate demand, imposing whatever dynamics of labor supply is restrictive to the model. Thus, as can be seen, vii despite being independent, all four chapters deal with the same theme and have a common objective.